Teoria de controle ótimo em sistemas abertos
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Data
2018-01-29
Autores
Cervati Neto, Alaor
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Editor
Universidade Estadual Paulista (Unesp)
Resumo
A teoria de informação e computação quântica é uma área de pesquisa que vem crescendo de maneira acentuada nos últimos anos devido aos inúmeros avanços tecnológicos que a acompanham. Neste mestrado começamos nossos estudos nesta área de pesquisa onde nos introduzimos e aprofundamos em seus aspectos intrigantes e peculiares. Dada nossa formação inicial na área de ciências da computação, inicialmente nos dedicamos a entender os aspectos fundamentais da mecânica quântica, assim como da teoria de informação e computação quântica. Focamos principalmente nos sistemas quânticos abertos, visto que o maior obstáculo a ser superado para o desenvolvimento destes computadores é o efeito deletério do meio ambiente. A princípio, concentramos nossos estudos nos ditos processos não-Markovianos, que apresentam efeitos de memória. Aprendemos sobre as novas medidas de não-Markovianidade, principalmente as medidas baseadas na dinâmica do emaranhamento e na dinâmica da informação mútua. Conseguimos publicar nosso primeiro resultado, onde provamos a inequivalência destas duas medidas de não-Markovianidade. De fato, mostramos que tais medidas, em geral, podem discordar sobre o tipo de processo dissipativo, sendo que uma pode reconhecê-lo como Markoviano enquanto outra pode reconhecê-lo como não-Markoviano. Como mostramos, esta inequivalência está diretamente relacionada com o refluxo de informação do meio ambiente para o sistema, e como mensuramos tal informação nestas duas medidas distintas de não-Markovianidade. Finalmente, na fase final de nossos estudos, tivemos como objetivo encontrar um meio de otimizar o controle das operações lógicas. Especificamente, trabalhamos com um método numérico utilizado em sistemas fechados para otimizar sistemas abertos Markovianos. Observamos que a eficácia deste método depende do tipo e intensidade da interferência do ambiente e das condições iniciais do sistema, obtendo melhores resultados em casos específicos.
Quantum information theory and computation is a field of research that has been growing acutely in the past few years due to the many technological improvements it follows. In this masters’ course, we began our studies in this area of research where we were introduced and immersed in its intriguing and peculiar aspects. Given our initial formation in computer science, we initially dedicated ourselves to understanding the fundamentals of quantum mechanics, as well as of information theory and quantum computation. Our main focus were open quantum systems, since the greatest obstacle to the development of these computers is the harmful effect of the environment. At first, we concentrated our studies in the so called non-Markovian processes, that show memory effects. We learned about the new non-Markovianity measurements, mainly those based on the dynamics of entanglement and mutual information. We managed to publish our first result, where we proved the inequivalence of these two measurements of non-Markovianity. Indeed, we showed that such measurements, in general, can disagree about the dissipative process, so that one can regard it as Markovian and the other as non-Markovian. As we demonstrated, this inequivalence is directly related to the information back-flow from the environment to the system, and how this information is measured by each of the two distinct measurements. Finally, in the last stage of our studies, our goal was to find a way to optimize the control of the logical operations. Specifically, we worked with a numeric method used in closed systems to optimize Markovian open systems. We have observed that the effectiveness of this method depends on the type and intensity of the interference of the environment and of its initial conditions, attaining better results for specific cases.
Quantum information theory and computation is a field of research that has been growing acutely in the past few years due to the many technological improvements it follows. In this masters’ course, we began our studies in this area of research where we were introduced and immersed in its intriguing and peculiar aspects. Given our initial formation in computer science, we initially dedicated ourselves to understanding the fundamentals of quantum mechanics, as well as of information theory and quantum computation. Our main focus were open quantum systems, since the greatest obstacle to the development of these computers is the harmful effect of the environment. At first, we concentrated our studies in the so called non-Markovian processes, that show memory effects. We learned about the new non-Markovianity measurements, mainly those based on the dynamics of entanglement and mutual information. We managed to publish our first result, where we proved the inequivalence of these two measurements of non-Markovianity. Indeed, we showed that such measurements, in general, can disagree about the dissipative process, so that one can regard it as Markovian and the other as non-Markovian. As we demonstrated, this inequivalence is directly related to the information back-flow from the environment to the system, and how this information is measured by each of the two distinct measurements. Finally, in the last stage of our studies, our goal was to find a way to optimize the control of the logical operations. Specifically, we worked with a numeric method used in closed systems to optimize Markovian open systems. We have observed that the effectiveness of this method depends on the type and intensity of the interference of the environment and of its initial conditions, attaining better results for specific cases.
Descrição
Palavras-chave
Computação quântica, Teoria da informação quântica, Sistemas quânticos abertos, Quantum computation, Quantum information theory, Open quantum systems